Video Transcript
Missing Numbers in Subtraction
Equations
In this video, we’re going to learn
how to find any missing number in a subtraction equation. And we’re going to do this when
we’re subtracting within 10.
Let’s start with this pile of
sweets. If we count them, we can see that
there are eight of them. If we were to start drawing a
part–whole model, we could say that the whole amount, the total amount, is
eight. Now let’s imagine that we take away
some of these sweets. Perhaps we’re feeling hungry and we
start munching. There we are. We’ve subtracted part of the whole
amount, and we have one, two, three sweets left. We could write this part that’s
been left behind on our part–whole model. We could even represent what’s just
happened as a number sentence.
We started with eight sweets. We then subtracted or took away a
number that we don’t know at the moment. And we’re left with three
sweets. Eight take away what equals
three. And this is exactly what we mean
when we talk about a subtraction equation with a missing number. And it’s this missing number that
we need to find. So what do we know?
Well, the first thing we know is
that the number of sweets we take away is going to leave us with three. And we also know that the number we
took away goes together with three to make eight. Let’s sketch our missing sweets
until we have eight. Remember, we already have
three. So we can start counting from
three: four, five, six, seven, eight. Three and one, two, three, four,
five go together to make a total of eight.
So now we can complete our missing
number. Eight take away five equals
three. Eight is the whole amount, three is
a part, and five is a part. If we’re left with three, we know
we must have taken away five.
Let’s look at some more subtraction
equations and try finding some more missing numbers.
Complete the following. Seven take away what is three.
In this question, we’re given a
subtraction with a missing number. We don’t know how many to take
away. But what do we know? Well, we’re told that seven take
away something equals three. And it’s our job in this problem to
work out what this missing number in our subtraction equation is.
Well, to help us with this problem,
we’ve got a picture to look at. It’s a picture of a group of
birds. How many birds are there
altogether? Let’s count them. There are one, two, three, four,
five, six, seven birds altogether. This is where the number seven
comes from in our number sentence. In a part–whole model, the number
seven represents the whole amount. It’s the total number of birds.
But if we look at our picture, we
can see that the whole amount has been split into two parts. Part of the group of birds have
flown the nest, and we can see that four birds have flown the nest. And if we count the part of the
group that haven’t flown the nest yet, we can see that this is three birds. In other words, our family of seven
birds has been split into a group of four and a group of three.
We can use this information to help
us solve the problem. Seven take away what leaves us with
three. Well, as we’ve said already, we
know that four and three go together to make seven. So, if we take away one, two,
three, four, just like the four birds that flew away, we’ll be left with three. Our missing number is four. Seven take away four is three.
Mason drew this model to check that
nine is the missing number in the equation. When he took away three from nine,
he was left with six. Nine take away three equals
six. Find the missing number in this
equation. Draw a model to check your
answer. What take away four equals two.
In this problem, we’re given a
subtraction number sentence or equation with a missing number in it. And that’s the first number. Something take away four is going
to leave us with two. Now, we’re told that we need to
draw a model to check our answer, and there are lots of models we could use. We could use counters or cubes. But instead let’s do what Mason did
and try to understand his model. Perhaps we could use Mason’s model
to help us answer our question.
We can see that the model that
Mason’s used is a little bit like a number track. It’s got lots of squares in a row,
and each one has got a different number in it. Now, if we look at the equation
that Mason has been trying to answer, we can see that there is a box around the
first number. This shows that this is the number
he was looking for. Probably when he started answering
the question, it looked like this. Something take away three equals
six. And Mason must have thought to
himself “Well, whatever the first number is, I know that if I take away three from
it, it’s going to leave me with six. So I’m going to start by drawing
those six squares that are going to be left.” And then we can imagine that he
thought to himself, “Well, these six are going to be left after I’ve taken away
three. So I need to put back the three
that I take away: one, two, three.”
You see, Mason understands that six
and three go together to make a whole amount. And it’s this whole amount that
he’s looking for. Six add another three makes seven,
eight, nine. So he can use this model to check
that the missing number was nine. Nine take away three equals
six.
Now that we understand Mason’s
model, let’s use it to check our own answer. What number if we take away four
from it will leave us with two? To begin with, let’s draw the two
that are going to be left behind. There we are, and we know that
these two are left behind after we’ve taken away four. So, next, we need to draw in the
four that we’ve taken away: one, two, three, four. We know that two and four are two
parts that go together to make a whole amount. And it’s this whole amount that
we’re looking for. We already have two. So let’s count on another four:
three, four, five, six. Our whole amount is worth six.
Now let’s check whether six take
away four leaves us with two. Yes, it does. Two is a part, four is a part, and
the whole amount is six. Six take away four equals two.
Fill in the blank. Seven take away what equals
two.
In this question, we’ve got a
subtraction number sentence or equation, but it’s got a missing number in it. And although the missing number is
often after the equal sign — we need to find the answer — in this question the
missing number is one of the numbers at the start. Seven take away what equals
two.
We could model this problem using
cubes. Here’s a line of seven cubes. This represents the whole
amount. It’s the number that we start with
in our subtraction. We could even sketch a part–whole
model and write the number seven in the place that represents the whole amount.
Now, our number sentence tells us
that we take away something — we don’t know what this number is — but that we’re
left with two. Let’s model the number of cubes
that we’re left with. Now, if these are the two cubes
that are left behind, the number that we’ve taken away must be the number that goes
together with two to make seven. In other words, seven is the whole
amount. Two is one of the parts. What’s the other part worth? What number goes with two to make
seven?
Let’s count on from two until we
get to seven and see how many cubes we add on: one, two, three, four, five. Five and two are two parts that go
together to make seven. So, if we start with seven and we
take away five, we’re going to be left with two. Our missing number is the number
five. And we can say seven take away five
equals two.
Now what have we learned in this
video? We’ve learned how to find any
missing number in a subtraction equation.
